Question

Find the limit

Answer 1

First split it into two fractions, then know that:

\[\lim_{x \rightarrow 0}\frac{ \sin(x) }{ x }=1 \]As long as the angle of sin and the thing in the denominator match, you can say that is 1.

Answer 2

@Psymon So far Im at this point, would the answer be 2?

Answer 3

Not quite. Usually they have you do a trick to force what you have to look like: sinx/x Now, x can be anything, as long as the angle of sin and the number in the denominator match. so yes, you have that left fraction that reduced to 2, but now you need to mess with the right fraction.

\[\frac{ -\sin(kx) }{ x }\]So since the angle of sin is kx, we need the denominator to be kx. So what do you have to do to get a k in the bottom?

Answer 4

@Psymon Ah I see. I would multiply k, Would the multiplication carry over to 2x/x as well?

Answer 5

nah, you dont need to do that, just keep it on the one fraction. So you would multiply top and bottom by k